So that applies to Vanguard or iShares ETF's?
These funds are actually separate trusts that "contract out" the administration/management/advertisement to whoever they are associated with. So iShares is offered by Barclay - and if the latter went bankrupt, iShares might start to be offered by Citibank. Barclay has no ownership of the trust, but does appoint the people who manage the trust.
Vanguard has a unique structure such that there is no conceivable risk of them even going bankrupt. And if they did go bankrupt for some inconceivable reason, you'd still be fine. The way they do it is they turn the usual model around: Vanguard doesn't own its funds, but its funds own Vanguard.
Each mutual fund is its own (separate) entity and in turn owns a part of the company Vanguard (where the share it holds depends on the funds' market capitalization). This works because Vanguard is essentially a member-owned collective: its fully owned by the customers, proportional to their investments held at Vanguard. Without outside investors (e.g. shareholders), they can structure themselves completely differently. The company Vanguard only has wage expenses, which are pretty predictable and fairly flexible - they're not susceptible to any market risk. But if they needed more cash and couldn't get loans, they could just raise ever so slightly the management fees to raise capital. But what if Vanguard did go bankrupt? Well, the funds are investors in the company, and investors (shareholders, if you will) have no obligation to bail them out. So this is similar to how it works with iShares.
The only downside to that structuring is that I have no clue how there is any oversight of the management team... I guess mutual fund holders can vote for the trustees of their fund? (I own ETFs, not mutual funds, from Vanguard.) Those trustees end up voting for the board of Vanguard. So, not surprisingly, there's great overlap between the people who are trustees of funds and people who are on the board of Vanguard. By and large, they write their own paychecks and do not disclose their salaries... At the end of the day, I only care about management fees and returns on the funds they provide. If they want to pay themselves a hundred million a year, I really couldn't care less. But I know people who go with the teacher/college employees' TIAA-CREF instead because they voluntarily disclose that information and give policyholders a consulting vote on executive pay.
In any case, there's great effort put into place to separate ETFs and Mutual Funds from the company that manages them. I don't see how the same is possible with an insurance product... health insurance, life insurance, annuity payments... all of those are subject to the institution not going bankrupt.
The way products like the one Burren mentioned are usually structured is that you pay $x to the insurance company, and they promise to make your future benefits contingent on market returns (usually with some upside and downside limits). But that's very different from putting your money into a trust that is a separate legal entity existing for the sole purpose of taking that money and investing it according to a predetermined strategy.
With annuities, people receiving payouts receive preferential treatment to other claims. However, when an insurance company goes bust, there's usually not a whole lot of assets around. Then some states promise various levels of coverage... but it's nothing comparable to the guarantee provided by the FDIC. For one, I don't even see how states could afford such a guarantee... a collapse of a company like AIG would be far too expensive even for the federal government. (Which, one might note, is why the latter does not promise such insurance - and why everything possible was done to prevent AIG from failing. That's where your car and life insurances and annuities are, and where the airlines' liability insurance is (I believe)... lose all that, and see how many services still operate.)